There are many ways to short term rates like
HW process. However I failed to understand how this information can be used to simulate the process for Overnight rate like
Can you please refer to any online technical papers to simulate such Overnight process?
Just to explain more, let say I define a HW process as follows
$dr(t) = (\theta(t)-\alpha r(t))dt+\sigma dW_t$
With this process, I can estimate a discount bond as $P(t, t+1)$ based on the estimated parameters (refer to https://en.wikipedia.org/wiki/Hull–White_model)
So is it right to day that the process for OI rate is just the process for $P(t,t+1)$?
Is there any software implementation like
R/Python that someone can please refer to?
Thank you very much.